1. Field of the Invention
The present invention relates to the field of Nuclear Magnetic Resonance logging of geological formations. Specifically, the invention is a method of phase-alternated RF induction of nuclear spins.
2. Description of the Related Art
A variety of techniques are utilized in determining the presence and estimation of quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, the resistivity, porosity and permeability of the rock formation surrounding the wellbore drilled for recovering the hydrocarbons. Typically, the tools designed to provide the desired information are used to log the wellbore. Much of the logging is done after the well bores have been drilled. More recently, wellbores have been logged while drilling, which is referred to as measurement-while-drilling (MWD) or logging-while-drilling (LWD).
One recently evolving technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things, porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of fluids in the geological formations surrounding the wellbore so that certain parameters such as spin density, longitudinal relaxation time (generally referred to in the art as T1) and transverse relaxation time (generally referred to as T2) of the geological formations can be measured. From such measurements, porosity, permeability and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
The NMR tools generate a uniform or near uniform static magnetic field in a region of interest surrounding the wellbore. NMR is based on the fact that the nuclei of many elements have angular momentum (spin) and a magnetic moment. The nuclei have a characteristic Larmor resonant frequency related to the magnitude of the magnetic field in their locality. Over time the nuclear spins align themselves along an externally applied magnetic field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field, which tips the spins with resonant frequency within the bandwidth of the oscillating magnetic field away from the static field direction. The angle θ through which the spins exactly on resonance are tipped is given by the equation:θ=γB1tp/2  (1)where γ is the gyromagnetic ratio, B1 is the magnetic flux density amplitude of the sinusoidally oscillating field and tp is the duration of the RF pulse.
After tipping, the spins precess around the static field at a particular frequency known as the Larmor frequency ω0, given byω=γB0  (2)where B0 is the static field intensity. At the same time, the spins return to the equilibrium direction (i.e., aligned with the static field) according to an exponential decay time known as the spin-lattice relaxation time or T1. For hydrogen nuclei, γ/2π=4258 Hz/Gauss, so that a static field of 235 Gauss would produce a precession frequency of 1 MHz. T1 of fluid in pores is controlled totally by the molecular environment and is typically ten to one thousand milliseconds in rocks.
At the end of a θ=90° tipping pulse, spins on resonance are pointed in a common direction perpendicular to the static field, and they precess at the Larmor frequency. However, because of inhomogeneity in the static field due to the constraints on tool shape, imperfect instrumentation, or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time long compared to the precession period, but shorter than T1, the spins will no longer be precessing in phase. This de-phasing occurs with a time constant that is commonly referred to as T2* if it is predominantly due to the static field inhomogeneity of the apparatus, and as T2 if it is due to properties of the material.
One method to create a series of spin echoes is due to Carr and Purcell. Discussed in Fukusima, E., and Roeder, B., “Experimental Pulse NMR: A Nuts and Bolts Approach”, 1981, as well as Slichter, C. P., “Principles of Magnetic Resonance”, 1990. The pulse sequence starts with a delay of several T1 to allow spins to align themselves along an applied static magnetic field axis. Then a 90° tipping pulse is applied to rotate the spins into the transverse plane, where they precess with angular frequency determined by local magnetic field strength. The spin system loses coherence in accordance with time constant, T2*. After a short time (tCP) a 180° tipping pulse is applied which continues to rotate the spins, inverting their position in the transverse plane. The spins continue to precess, but now their phases converge until they momentarily align a further time tCP after application of the 180° pulse. The realigned spins induce a voltage in a nearby receiving coil, indicating a spin echo. Another 180° pulse is applied after a further time tCP, and the process is repeated many times, thereby forming a series of spin echoes with spacing 2 tCP.
While the Carr-Purcell sequence would appear to provide a solution to eliminating apparatus induced inhomogeneities, it was found by Meiboom and Gill that if the duration of the 180° pulses in the Carr-Purcell sequence were even slightly erroneous so that focusing is incomplete, the transverse magnetization would steadily be rotated out of the transverse plane. As a result, substantial errors would enter the T2 determination. Thus, Meiboom and Gill devised a modification to the Carr-Purcell pulse sequence such that after the spins are tipped by 90° and start to de-phase, the carrier of the 180° pulses is phase shifted by π/2 radians relative to the carrier of the 90° pulse. This phase change causes the spins to rotate about an axis perpendicular to both the static magnetic field axis and the axis of the tipping pulse. If the phase shift between tipping and refocusing pulses deviates slightly from π/2 then the rotation axis will not be perfectly orthogonal to the static and RF fields, but this has negligible effect. For an explanation, the reader is referred to a detailed account of spin-echo NMR techniques, such as in Fukushima and Roeder, “Experimental Pulse NMR: A Nuts and Bolts Approach”. As a result any error that occurs during an even numbered pulse of the CPMG sequence is cancelled out by an opposing error in the odd numbered pulse. The CPMG sequence is therefore tolerant of imperfect spin tip angles. This is especially useful in a well logging tool which has inhomogeneous and imperfectly orthogonal static and pulse-oscillating (RF) magnetic fields.
A typical CPMG sequence is shown in FIG. 2. Excitation pulse 201 rotates the magnetic spins into the xy-plane. Refocusing pulses (202a, 202b, 202c, 202d, 202e  . . . ) are applied following the excitation pulse, each of which induce a spin echo (203a, 203b, 203c, 203d, 203e . . . ). Although the illustration of FIG. 2 is limited to five refocusing pulses, in reality there can be hundreds or thousands of pulses and echoes. The time between the centers of two subsequent echoes is called inter-echo spacing TE. The curve linking the echo maxima is the echo decay curve 210. All refocusing pulses have the same phase. The phase of the excitation pulse is offset by either +90° or −90°. Some characteristics of the CPMG sequence are:    a) The excitation pulse tips the z-magnetization (aligned with the static magnetic field) into the xy-plane perpendicular to the z-axis.    b) The refocusing pulses rotate the magnetization by 180°.    c) If all pulses have the same amplitude, then refocusing pulses are twice the length of the excitation pulse.    d) All refocusing pulses have the same phase, but the excitation pulse phase is 90° different.The last characteristic d) was the novelty when the CPMG was first published. This phase shift between excitation pulse and refocusing pulses causes a compensation of rephasing angle errors. With the phase shift the errors correct themselves with every second echo.
As noted above, the CPMG sequence tolerates imperfect spin tip angles. As an example, U.S. Pat. No. 6,466,013, to Hawkes et al. discusses a method, referred to as the Optimized Rephasing Pulse Sequence (ORPS), which optimizes the timings for inhomogeneous B0 and B1 fields to obtain maximum NMR signal or, alternatively, to save radio frequency power. A pulsed RF field is applied which tips the spins on resonance by the desired tip angle for maximum signal, typically 90° tipping pulse. A refocusing pulse having a spin tip angle substantially less than 180° is applied with carrier phase shifted by typically π/2 radians with respect to the 90° tipping pulse. Although the refocusing pulses result in spin tip angles less than 180° through the sensitive volume, their RF bandwidth is closer to that of the original 90° pulse. Hence more of the nuclei originally tipped by 90° are refocused, resulting in larger echoes than would be obtained with a conventional 90° refocusing pulse. ORPS is not a CPMG sequence. The timing and duration of RF pulses are altered from conventional CPMG to maximize signal and minimize RF power consumption. Nevertheless ORPS still possesses the characteristic d), i.e. the excitation pulse is phase shifted by 90° with respect to the refocusing pulses. An additional forced recovery pulse at the end of an echo train may be used to speed up the acquisition and/or provide a signal for canceling the ringing artifact.
The NMR echoes of an echo sequence like CPMG or ORPS contain, in addition to the true NMR signal, DC offset and ringing. Radio frequency pulses typically cause ringing (magneto-acoustic, electronic) after each pulse. This ringing can be larger than the NMR signal itself. It must be avoided or subtracted before further processing of the NMR data. DC offset of the NMR signals must also be determined and subtracted. We refer to the DC offset and ringing as non-NMR signals to distinguish them from NMR signals from nuclei in earth formations.
Subtraction methods for reducing ringing and offset are known in the prior art. The standard method for this is the use of a Phase Alternated Pair (PAP) of echo sequences.
In order to cancel the electronic offsets and antenna ringing, it is customary to combine two CPMG measurements of opposite phase. These pairwise-combined measurements are called phase-alternate-pair (PAP) echo trains and these constitute the datasets that are submitted to processing. U.S. Pat. No. 6,624,629, to Kleinberg et al., discusses a standard PAP method. In a PAP sequence, two CPMG or ORPS sequences are acquired. In one sequence, the excitation pulse rotates the nuclear spins by −90° with respect to the refocusing pulses, and in the other sequence, the excitation pulse rotates the nuclear spin by +90° with respect to the refocusing pulses. The inverted phase of the alternate excitation pulse causes a phase inversion of all the echoes. Meanwhile the effects of ringing due to the refocusing pulses are unaffected by the inversion of the excitation pulses. A typical PAP sequence is shown in FIG. 3. By subtracting the acquired echo data of the lower sequence of FIG. 3 from those of the upper sequence, the ringdowns of all refocusing pulses and the offsets are subtracted while the NMR echoes are added.
A condition for proper ringdown and offset subtraction of the PAP is that the ringdown and offset are repeatable, i.e. identical in both sequences that make up the PAP.
U.S. Pat. No. 6,522,138, to Heaton and U.S. Pat. No. 6,525,534, to Akkurt et al. discusses method of reducing ringing effects. Heaton '138 discusses retrieving corrected individual measurements from sequentially parwise-combined measurements. Such sequentially pairwise-combined measurements may include PAP NMR measurements from well logging. One of the methods comprises providing an initial estimate for a first one of the corrected individual measurement, deriving temporary estimates for other ones of the corrected individual measurements by subtracting the initial estimate from the first sequentially pairwise-combined measurements to produce an estimate for a second one of the corrected individual measurements, and repeating the subtraction from each of the next sequentially pairwise-combined measurements until temporary estimates for each of the corrected individual measurements are obtained, and correcting errors in the temporary estimates to generate error-corrected estimates by filtering an alternating error component associated with the initial estimate. Akkurt '534 discusses improving the vertical resolution of NMR logs based on data acquisition methods and signal processing techniques that need not apply PAPS. The method of Akkurt '534 is based on reducing the level of coherent non-formation signals, but providing estimates of these signals and removing the estimates from the underlying NMR pulse echo trains.
Alternate methods for improving resolution are discussed in the prior art. U.S. Patent Appl. No. 2004/0008027, of Prammer, discusses providing, in a geologic formation, at least one first plurality of phase alternated NMR pulses at a first frequency (F1), and receiving at least one corresponding first signal in response. The method includes providing, not necessarily simultaneously, at least one second plurality of phase alternated NMR pulses at a second frequency (F2), and receiving at least one corresponding second signal in response thereto. In an embodiment of Prammer a difference between the first and second frequencies is a function of one or more of an inter-echo spacing, a time delay between and excitation pulse and a data acquisition window, and a rate for generating echoes. The received first and second signals are combined to obtain a corrected NMR signal.
U.S. Pat. No. 6,624,629, to Speier et al., uses a controller adapted to cause the RF transmitter to transmit RF pulse sequences into a sample and for each different RF pulse sequence, vary an estimated pulse width for producing a predetermined flip angle by a different scaling facto to produce flip angles near the predetermined flip angle. The controller is adapted to receive spin echo signals in response to the transmission of the RF pulse sequences; determine a property of the sample in response to the spin echo signals; and use the spin echo signals to determine an optimal pulse width for producing the predetermine flip angle.
The technique of PAP depends on the repeatability of offset and ringing. Between the acquisition of the two echo sequences may be a remagnetization delay of up to 10 seconds. In reality, both offset and ringing may not be stable over such a long time. Yet another disadvantage of PAP is that a complete NMR measurement takes at least two echo sequences with a (long) remagnetization time between them. For fast NMR (wireline) logging this is a disadvantage because the aperture of the NMR measurement along the borehole axis is increased. Therefore there are quite a number of reasons to look for alternatives to PAP for subtracting offset and ringing from the NMR signal. The present invention fulfills those needs.